Pith Number

pith:PSEJT6MQ

pith:2026:PSEJT6MQW3I5C47L3HXICJBHPN

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Model Checking for Regressions Based on Weighted Residual Processes with Diverging Number of Predictors

Haiqi Li, Xintao Xia, Yue Hu

Weighted residual processes yield a valid specification test for parametric regressions when the number of predictors diverges with sample size.

arxiv:2604.14649 v2 · 2026-04-16 · stat.ME · math.ST · stat.TH

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Claims

C1strongest claim

We propose a new specification test based on weighted residual processes for evaluating the parametric form of the regression mean function in high-dimensional settings where the number of predictors increases with the sample size. We establish the asymptotic properties of the test statistic under the null hypothesis and under global and local alternatives. The proposed test maintains the nominal significance level and can detect local alternatives that deviate from the null hypothesis at the parametric rate 1/√n. Furthermore, we propose a smooth residual bootstrap to approximate the limiting null distribution and establish its validity in high-dimensional settings.

C2weakest assumption

The approach relies on unspecified regularity conditions and rates for the diverging dimension p_n relative to n that allow the weighted residual process to have non-degenerate limits and the bootstrap to be consistent; these are invoked for the asymptotic theory but not detailed in the abstract.

C3one line summary

A new test based on weighted residual processes with smooth bootstrap maintains correct size and detects local alternatives at rate 1/sqrt(n) for regression model checking when predictor dimension diverges with sample size.

Receipt and verification

First computed	2026-07-22T00:22:34.428185Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7c8899f990b6d1d173ebd9ee8124277b75e35b29e2673d77e50d21e28a956d14

Aliases

arxiv: 2604.14649 · arxiv_version: 2604.14649v2 · doi: 10.48550/arxiv.2604.14649 · pith_short_12: PSEJT6MQW3I5 · pith_short_16: PSEJT6MQW3I5C47L · pith_short_8: PSEJT6MQ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/PSEJT6MQW3I5C47L3HXICJBHPN \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 7c8899f990b6d1d173ebd9ee8124277b75e35b29e2673d77e50d21e28a956d14

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f164eabb1fcb31773911a95a6e95ce6081c3f543d206d046af34a7964f47ceec",
    "cross_cats_sorted": [
      "math.ST",
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "stat.ME",
    "submitted_at": "2026-04-16T05:55:37Z",
    "title_canon_sha256": "85e20480d0b05b810a0acad5ba9b9c156f2a97e491a480c05eefd022d2bca178"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.14649",
    "kind": "arxiv",
    "version": 2
  }
}